Electronic – Controlling which transistor turns on first in a multivibrator

The way to solve such problems is to slightly alter the symmetry of the circuit in such a way that, at power-on, there is a chosen BJT that is off while the other two are in saturation, as Tony Stewart implicitly suggested. You could achieve this by placing a resistor \$R_{set}\$ in parallel to the base resistor R of the two BJTs you want to be in saturation "immediately after" power-up:

^{simulate this circuit – Schematic created using CircuitLab}

However this method causes the slight decrease of two of the three time constants of the circuit. If you do not want to do that, another method is to use a \$R_{set}\$ base resistor to keep the chosen BJT out of saturation at power-on:

^{simulate this circuit}

Knowing resistor tolerances and the transistor parameters and parameter spreads, you can calculate the maximum/minimum values required for the resistor \$R_{set}\$: a basic procedure is described below.

A quantitative description

At power-up, in the case of perfectly identical circuits, each transistor \$Q\$ sees the capacitor \$C\$ as a short circuit. Thus, for each transistor we have $$ V_{BE}=V_{CE}\:\text{ at }\:t=t_0 \tag{1} \label{1} $$ i.e. every transistor at power up is in the active region (i.e. not in saturation). As times goes, each capacitor \$C\$ is charged by the resistor \$R\$ in an approximately (but up to a high precision) linear way with a charging current \$I_\mathrm{crg}\$ whose value is $$ I_\mathrm{crg}\approx\frac{V_{CC}-V_{BE}}{R}\approx\frac{4.5V-0.7V}{4700\Omega} \tag{2} \label{2} $$ Since \$V_{BE}\$ cannot vary too much, \$C\$ rises the voltage between its plates at the expenses of the \$V_{CE}\$ until $$ V_{CE}=V_{CE_\mathrm{sat}} \tag{3} \label{3} $$ In the standard two-BJTs circuit, as the one you analyzed in your first simulation is, this is the start-up of the oscillation: the positive feedback of the two cascaded BJT stages amplifies the ubiquitous noise and brings one of the BJTs in saturation, while the other goes off. Therefore, to make sure that a chosen device is off (and thus, in this case, light the LED) when the others have been in saturation, you have to be sure that the condition \eqref{3} is verified for it only after it has been verified for the other. You can satisfy this requirement in two ways,

1. by slightly increasing \$I_\mathrm{crg}\$ \eqref{2} for the remaining devices: this is simply accomplished by placing a resistor in parallel to \$R\$ for all other base biasing circuits,
2. or by slightly increasing the \$V_{CE}\$ voltage of the chosen one, putting a resistor in series to its base terminal in order to have $$ V_{CE}=V_{BE}+R_{set}I_B\:\text{ at }\:t=t_0, \tag{4} \label{4} $$ thus verifying \eqref{3} at later times, due to the higher initial value of \$ V_{CE}\$. In this last case you can chose \$R_{set}\$ to be $$ R_{set}\geq\frac{V_{BE_\mathrm{sat}}-V_{CE_\mathrm{sat}}}{I_\mathrm{crg}}, \tag{5} \label{5} $$ the "\$\geq\$" sign meaning that this value should be greater than the uncertainty on \$R\$ due to the unavoidable resistor tolerances.

Some notes

• The values \$V_{BE_\mathrm{sat}}\$ and \$V_{CE_\mathrm{sat}}\$ should be read from the datasheet of \$Q\$ and depend on \$I_{B_\mathrm{sat}}\$ and on \$I_{C_\mathrm{sat}}\$. However you can safely assume that $$ V_{BE_\mathrm{sat}}=0.7V\quad V_{CE_\mathrm{sat}}=0.25V $$ I advice you to put the value of \$R_{set}\$ calculated by \eqref{5} in series to the SPICE circuit of the two-BJTs circuit in order to see the above described behavior.
• There is a problem in your three-BJTs circuit: as the spice simulation confirm, the feedback is negative at DC to low frequency, therefore it cannot start oscillating. Your breadboard prototype works because it probably behaves like a phase-shift oscillator, each of the three stages providing a phase shift of nearly 60° to a (very) approximatively sinusoidal oscillation, which is clamped by the LED diodes. If you want it to behave like a multivibrator, you have to add a further BJT stage (without timing tank i.e. without \$C\$, if you need to light only three LED) in order to have a DC positive feedback.